Compatibility between finite volumes and finite elements using solutions of shallow water equations for substance transport

This paper formulates a finite volume analogue of a finite element schematization of three‐dimensional shallow water equations. The resulting finite volume schematization, when applied to the continuity equation, exactly reproduces the set of matrix equations that is obtained by the application of t...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2007-03, Vol.53 (9), p.1495-1507
Main Authors: Postma, Leo, Hervouet, Jean-Michel
Format: Article
Language:English
Subjects:
Applied sciences
Computational methods in fluid dynamics
continuity equation
Exact sciences and technology
finite element method
finite volume method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Physics
pollutant transport
Pollution
surface water flow
Water treatment and pollution
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Summary:This paper formulates a finite volume analogue of a finite element schematization of three‐dimensional shallow water equations. The resulting finite volume schematization, when applied to the continuity equation, exactly reproduces the set of matrix equations that is obtained by the application of the corresponding finite element schematization to the continuity equation. The procedure allows the consistent and mass conserving coupling of the finite element Telemac model for three‐dimensional flow with the finite volume Delft3D‐WAQ model for water quality. The work has been carried out as part of a joint development by LNHE and WL∣Delft Hydraulics to explore the mutual interaction of their software. Copyright © 2006 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.1373